Cette thèse traite des langages reconnaissables de mots indexés par des ordinaux.<br /><br />Plusieurs classes d'automates qui reconnaissent de tels mots ont été introduites par Büchi. Elles diffèrent par la longueur des mots reconnus par les automates. Nous en utilisons quatre: la classe pour les mots de longueur [$\omega$] , celle pour les mots de longueur inférieure à [$\omega^(n+1)$] , où n est un entier naturel, celle pour les mots de longueur dénombrable, et celle pour les mots de longueur quelconque. Nous y ajoutons la classe des automates de Kleene traditionnelle, sur les mots finis. Nous remontrons que ces différentes définitions d'automates sont équivalentes, c'est-à-dire que données deux de ces classes et un automate d'une des deux, la restriction du langage reconnu par l'automate aux mots du domaine le plus petit des deux classes est la restriction du langage reconnu par un automate de l'autre classe au même domaine. Nous donnons également une présentation unifiée de la déterminisation pour chacune des classes qui reconnaît au plus des mots de longueur dénombrable.<br /><br />Les semigroupes finis sont un formalisme équivalent aux automates pour définir des ensembles de mots finis. Perrin, Pin et Wilke ont introduits des structures algébriques adaptées à l'étude des langages de mots de longueur [$\omega$] , qui, quand elles sont finies, sont équivalentes aux automates. Nous généralisons l'approche algébrique de la théorie des langages reconnaissables de mots de longueur [$\omega$] aux mots de longueur inférieure à [$\omega^(n+1)$] , puis aux mots de longueur dénombrable. Pour cela, nous définissons deux structures algébriques, les [$\omega^n$] -semigroupes et les [$\omega_1$] -semigroupes, qui, quand elles sont finies, sont équivalentes respectivement aux automates pour les mots de longueur inférieure à [$\omega^(n+1)$] et aux automates pour les mots de longueur dénombrable. Comme pour le cas des mots de longueur [$\omega$] , une algèbre syntaxique peut être canoniquement associée à chaque langage reconnaissable. Nous définissons le produit de Schützenberger et le produit en couronne sur les [$\omega_1$] -semigroupes. Nous étendons également le théorème des variétés d'Eilenberg aux mots de longueur dénombrable.<br /><br />Finalement, nous remontrons l'équivalence entre langages reconnus par automates et langages définis par énoncés de logique monadique du second ordre quand on s'intéresse aux mots de longueur dénombrable. Le théorème d'équivalence de Schützenberger entre langages sans étoile et semigroupes finis apériodiques est étendu aux mots de longueur inférieure à [$\omega^(n+1)$] , et le théorème d'équivalence entre langages sans étoile et langages définis par énoncés de logique du premier ordre de l'ordre linéaire de McNaughton et Papert est étendu aux mots de longueur quelconque.

abstract: Mixture experiments are useful when the interest is in determining how changes in the proportion of an experimental component affects the response. This research focuses on the modeling and design of mixture experiments when the response is categorical namely, binary and ordinal. Data from mixture experiments is characterized by the perfect collinearity of the experimental components, resulting in model matrices that are singular and inestimable under likelihood estimation procedures. To alleviate problems with estimation, this research proposes the reparameterization of two nonlinear models for ordinal data -- the proportional-odds model with a logistic link and the stereotype model. A study involving subjective ordinal responses from a mixture experiment demonstrates that the stereotype model reveals useful information about the relationship between mixture components and the ordinality of the response, which the proportional-odds fails to detect. The second half of this research deals with the construction of exact D-optimal designs for binary and ordinal responses. For both types, the base models fall under the class of Generalized Linear Models (GLMs) with a logistic link. First, the properties of the exact D-optimal mixture designs for binary responses are investigated. It will be shown that standard mixture designs and designs proposed for normal-theory responses are poor surrogates for the true D-optimal designs. In contrast with the D-optimal designs for normal-theory responses which locate support points at the boundaries of the mixture region, exact D-optimal designs for GLMs tend to locate support points at regions of uncertainties. Alternate D-optimal designs for binary responses with high D-efficiencies are proposed by utilizing information about these regions. The Mixture Exchange Algorithm (MEA), a search heuristic tailored to the construction of efficient mixture designs with GLM-type responses, is proposed. MEA introduces a new and efficient updating formula that lessens the computational expense of calculating the D-criterion for multi-categorical response systems, such as ordinal response models. MEA computationally outperforms comparable search heuristics by several orders of magnitude. Further, its computational expense increases at a slower rate of growth with increasing problem size. Finally, local and robust D-optimal designs for ordinal-response mixture systems are constructed using MEA, investigated, and shown to have high D-efficiency performance. / Dissertation/Thesis / Doctoral Dissertation Industrial Engineering 2016

Made available in DSpace on 2014-06-12T17:16:02Z (GMT). No. of bitstreams: 2 arquivo2850_1.pdf: 1952276 bytes, checksum: d682fd2d8fe8ba7babfed4aa04c97760 (MD5) license.txt: 1748 bytes, checksum: 8a4605be74aa9ea9d79846c1fba20a33 (MD5) Previous issue date: 2011 / Faculdade de Amparo à Ciência e Tecnologia do Estado de Pernambuco / Esta tese tem como objetivo geral analisar a qualidade das relações de transação existentes entre os pequenos produtores de frutas localizados no Polo Petrolina-Juazeiro e os agentes localizados logo à sua frente no canal de distribuição das frutas, identificando os principais fatores que determinam as relações vigentes observadas. Para tal, são utilizados como base os pressupostos e parâmetros básicos da Teoria da Economia dos Custos de Transação (ECT). Para se alcançar tais objetivos, a tese foi dividida em três estudos focais que se complementam em termos metodológicos e de argumentação. No primeiro foi realizada uma resenha dos principais trabalhos que utilizam a ECT como ferramenta para a análise das transações dos pequenos produtores no setor de frutas no país. Com isso, procurou-se gerar uma base teórica sólida para a sequência da análise proposta. No segundo foi dada atenção especial às relações transacionais existentes no agronegócio da fruta do Polo, destacando aquelas localizadas à jusante do processo produtivo e diretamente ligadas aos pequenos produtores. Feito isso, ainda nesta segunda seção, buscou-se relacionar a realidade local aos atributos descritos pela ECT como fundamentais na determinação das estruturas de governanças observadas entre os agentes. Por fim, foram analisados os principais fatores determinantes dos arranjos contratuais vigentes entre os pequenos produtores do Polo e seus elos à jusante, utilizando-se de variáveis que representam as dimensões particulares referentes à atividade da fruticultura e consideradas pela ECT. Para tal, foi lançado mão de um modelo de regressão logística ordinal e de dados obtidos em pesquisa de campo. Como resultado, no geral, observou-se haver no Polo uma relação positiva entre a maior parte das variáveis testadas e associada ao arcabouço teórico da ECT e a probabilidade do pequeno produtor de fruta do Polo variar a sua intensidade de coordenação vertical junto a seu elo à jusante. Deste modo, aqueles produtores que possuem um maior grau de especificidade e atributos, dentre os considerados pela ECT, acabam tendo também uma maior capacidade relativa de transacionar suas frutas por meio de estruturas de governança mais intensificadas, impedindo, como consequência, que os canais de comercialização utilizem de forma mais intensa seus poderes de barganha

Submitted by Israel Vieira Neto (israel.vieiraneto@ufpe.br) on 2015-03-04T14:13:21Z No. of bitstreams: 2 sammara_dissertacao.pdf: 1933363 bytes, checksum: 3948f7476054b8942a7b9c663ee83684 (MD5) license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) / Made available in DSpace on 2015-03-04T14:13:21Z (GMT). No. of bitstreams: 2 sammara_dissertacao.pdf: 1933363 bytes, checksum: 3948f7476054b8942a7b9c663ee83684 (MD5) license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) Previous issue date: 2012-08-10 / O primeiro ensaio propõe uma nova abordagem para estimar desigualdades socioeconômicas na Saúde Auto Avaliada. O método baseia-se em uma aplicação alternativa do Coeficiente de Gini, preservando a natureza categórica da variável e evitando incorrer nas dificuldades e limitações de cardinalizar tal indicador de saúde para análises de desigualdade. O proposto “Index-D” aplica as probabilidades preditas de um Modelo Probit Ordinal, sob a equação de Gini formatada para funções densidade discretas, permitindo-nos estimar variações na Saúde Auto Avaliada segundo subjacentes variações socioeconômicas e demográficas. Usamos dados da Pesquisa Nacional por Amostra de Domicílio (PNAD) para os anos de 1998, 2003 e 2008, apenas referente à população feminina, a fim de ilustrar a aplicabilidade do método. Os resultados mostram que a desigualdade em Saúde Auto Avaliada no Brasil decresceu de 1998 a 2008 entre as mulheres, independentemente do perfil socioeconômico considerado. Ainda, os grupos femininos com melhores condições financeiras apresentaram índices de desigualdade menores, enquanto que os mais pobres obtiveram os maiores escores. Considerando a desigualdade entre as Regiões, sudeste apresentou os resultados mais favoráveis, enquanto o Norte e o Nordeste reportaram as mais altas desigualdades, independentemente do ano e do perfil socioeconômico considerado. O segundo ensaio visa identificar o quanto da variância observada na Saúde Auto Avaliada (SAH) no Brasil é resultado do contexto onde as pessoas vivem. Dessa forma, através do Random-Intercept Ordered Probity Model, aplicamos uma amostra de municípios, retirada da Pesquisa Nacional por Amostra de Domicílios (PNAD), 2008, para representar as unidades do segundo nível, juntamente com as informações socioeconômicas dos indivíduos, a fim de controlar apropriadamente o efeito composição. Apesar de pequeno, o coeficiente de variação mostra a existência de variação sistemática na Saúde Auto Reportada entre os municípios urbanos do Brasil que persistiram mesmo após o controle do nível individual. As evidências sugerem que políticas de saúde no Brasil não devem investir apenas nas circunstâncias a nível individual, mas também sobre os ambientes sociais e físicos do coletivo, tais como segurança, espaços para lazer e infraestrutura urbana.

Fictitious play is a classical learning process for games, and games with strategic complementarities are an important class including many economic applications. Knowledge about convergence properties of fictitious play in this class of games is scarce, however. Beyond games with a unique equilibrium, global convergence has only been claimed for games with diminishing returns [V. Krishna, Learning in games with strategic complementarities, HBS Working Paper 92-073, Harvard University, 1992]. This result remained unpublished, and it relies on a specific tie-breaking rule. Here we prove an extension of it by showing that the ordinal version of strategic complementarities suffices. The proof does not rely on tie-breaking rules and provides some intuition for the result.

Fictitious Play is the oldest and most studied learning process for games. Since the already classical result for zero-sum games, convergence of beliefs to the set of Nash equilibria has been established for several classes of games, including weighted potential games, supermodular games with diminishing returns, and 3×3 supermodular games. Extending these results, we establish convergence of Continuous-time Fictitious Play for ordinal potential games and quasi-supermodular games with diminishing returns. As a by-product we obtain convergence for 3×m and 4×4 quasi-supermodular games.

The aim of this work is to decide the real usage of logistic regression in the market research tasks respecting the needs of final users of research results. The main argument for the final decision is the comparison of its output to the output of an alternative classification method used in practice -- a classification tree method. The topic is divided into three parts. The first part describes the theoretical framework and approaches linked to logistic regression (chapter 2 and 3). The second part analyses the experience with the usage of logistic regression in Czech market research companies (chapter 4) and the topic is closed by applying the method on real data and comparing the output to the classification tree output (chapter 5 and 6).

Background: Investigators are often interested in using population-level health administrative data in inflammatory bowel disease (IBD) patients to study disease outcomes, risk factors and treatment effects to enhance knowledge, shape clinical practice and influence health care policy. A major limitation of using health administrative data for these purposes is the lack of detailed clinical data to adjust for the confounding effects of differential disease severity on observed associations. Methods to account for disease severity using administrative variables would offer a major advance to population-level studies in IBD patients. Thus, in this study we aimed to use a cohort of IBD patients from The Ottawa Hospital (TOH) to validate a model that was originally developed in Manitoba for estimating clinical disease course in IBD patients through healthcare utilization measures. Objectives: The objectives of this thesis are: 1) To identify and characterize a reference cohort of IBD patients in the ambulatory clinics of four gastroenterologists from TOH on clinical disease course in the preceding year (reference cohort), based on a Manitoba definition of clinical disease course; 2) To fit a partial proportional odds (PPO) model for predicting IBD course, derived using Manitoba health administrative data, to the reference cohort of IBD patients using Ontario health administrative data; 3) To derive new PPO models of IBD disease course for the reference cohort using Ontario administrative variables and compare model performance; and 4) To apply the models to the Ontario Crohn’s and Colitis cohort (OCCC) to estimate IBD course in Ontario, and compare the distribution to that of the Manitoba IBD population.Methods: We first identified a reference cohort of IBD patients in Ontario from the outpatient clinics at TOH during fiscal year 2015. Through chart review, we classified these patients into one of four clinical disease categories (remission, mild, moderate, or severe) using the Manitoba definition. We linked these patients to Ontario health administrative datasets. Given slight differences in data structure and coding between Manitoba and Ontario, we were unable to directly test the Manitoba model and instead fit a PPO model to the Ontario cohort using analogous administrative variables to those used in the final Manitoba model (“adapted model”). We subsequently derived new PPO models using unique Ontario administrative variables under three strategies: 1) Stepwise variable selection (“stepwise model”); 2) Forced fitting of all variables (“all-variables model”); and 3) Using a two-step modelling algorithm that considered IBD-related hospitalizations separate from other administrative variables (“two-step model”). We then compared model performance from the four strategies. Finally, we applied the models to the Ontario IBD population from 2004 to 2016 and compared model estimates to those from Manitoba. Results: We identified 963 patients with IBD from TOH outpatient clinics, of which 52.3% (n=504) were males, 64.6% (n=622) had Crohn's Disease, and 89.2% (n=859) resided in an urban setting. Based on the Manitoba definition, 64.9% of patients within our reference cohort were classified as remission, while 11.4%, 14.1%, and 9.6% were classified as mild, moderate, and severe disease course, respectively. The adapted model (c-statistic 0.77, goodness-fit p-value 0.28) performed comparably to the other models: the stepwise model (c-statistic 0.77, goodness-fit p-value 0.50), the all-variables model (c-statistic 0.77, goodness-fit p-value 0.53), and the two-step model (c-statistic 0.78, goodness-fit p-value 0.75). The adapted model also resulted in overall similar estimates with regards to the disease course distribution among the Ontario IBD population. However, on closer inspection, our two-step model, in which individuals who had been hospitalized for an IBD-related indication within the past year were assumed to have severe disease, performed better with respect to accurately classifying individuals with moderate or severe disease, without sacrificing discriminative ability. Based on the two-step model, from 2004 to 2016, 89.2-91.2% of the Ontario IBD population was in remission, 0% had mild disease, 2.4-3.2% had moderate disease, and 5.9-8.4% had severe disease. Distribution of disease course among IBD patients in Ontario differed considerably than that in Manitoba. Conclusion: In the absence of clinical information within health administrative data, we present and compare four different models that can be used to partially account for the confounding effect of disease course among IBD patients in future population-based studies using Ontario health administrative data. Given that our models did not perform as originally expected, especially with regards to accurately identifying individuals with more active disease states, we advise researchers to use these models at their own discretion.

This thesis focuses on the less studied electoral systems, which are called ordinal. These methods allow the voters to order the candidates according to their preferences. The work provides a historical insight into this issue with regard to economics and political science theories, based on the concept of the Condorcet winner. Condorcet winner is the person who defeats all other candidates in pairwise elections and by theorists of the electoral system is the ability to choose the Condorcet winner essential. The work examines three electoral methods - alternative and suplementary vote and Borda rule. These electoral systems are analyzed in terms of effects to system of political parties, political actors and the electorate, with the emphasis on the utilization rate of preferential votes. These aspects are examined on the basis of the actual election results obtained from the website of the electoral commissions and independent institutions. Based on these data, a mathematical model that compares the effects of electoral systems is then created. The conclusion summarizes the results of the analysis and the author expresses further recommendations to address these electoral methods, not only professionally and scientifically, but also as real alternatives for real election.

Jusqu'à l'avènement de méthodes de neuroimagerie non invasives les connaissances du cerveau sont acquis par l'étude de ses lésions, des analyses post-mortem et expérimentations invasives. De nos jours, les techniques modernes d'imagerie telles que l'IRMf sont capables de révéler plusieurs aspects du cerveau humain à une résolution spatio-temporelle progressivement élevé. Cependant, afin de pouvoir répondre à des questions neuroscientifiques de plus en plus complexes, les améliorations techniques dans l'acquisition doivent être jumelés à de nouvelles méthodes d'analyse des données. Dans cette thèse, je propose différentes applications de l'apprentissage statistique au traitement des données d'IRMf. Souvent, les données acquises par le scanner IRMf suivent une étape de sélection de variables dans lequel les cartes d'activation sont extraites du signal IRMf. La première contribution de cette thèse est l'introduction d'un modèle nommé Rank-1 GLM (R1-GLM) pour l'estimation jointe des cartes d'activation et de la fonction de réponse hémodynamique (HRF). Nous quantifions l'amélioration de cette approche par rapport aux procédures existantes sur différents jeux de données IRMf. La deuxième partie de cette thèse est consacrée au problème de décodage en IRMf, ce est à dire, la tâche de prédire quelques informations sur les stimuli à partir des cartes d'activation du cerveau. D'un point de vue statistique, ce problème est difficile due à la haute dimensionnalité des données, souvent des milliers de variables, tandis que le nombre d'images disponibles pour la formation est faible, typiquement quelques centaines. Nous examinons le cas où la variable cible est composé à partir de valeurs discrets et ordonnées. La deuxième contribution de cette thèse est de proposer les deux mesures suivantes pour évaluer la performance d'un modèle de décodage: l'erreur absolue et de désaccord par paires. Nous présentons plusieurs modèles qui optimisent une approximation convexe de ces fonctions de perte et examinent leur performance sur des ensembles de données IRMf. Motivé par le succès de certains modèles de régression ordinales pour la tâche du décodage basé IRMf, nous nous tournons vers l'étude de certaines propriétés théoriques de ces méthodes. La propriété que nous étudions est connu comme la cohérence de Fisher. La troisième, et la plus théorique, la contribution de cette thèse est d'examiner les propriétés de cohérence d'une riche famille de fonctions de perte qui sont utilisés dans les modèles de régression ordinales. / Until the advent of non-invasive neuroimaging modalities the knowledge of the human brain came from the study of its lesions, post-mortem analyses and invasive experimentations. Nowadays, modern imaging techniques such as fMRI are revealing several aspects of the human brain with progressively high spatio-temporal resolution. However, in order to answer increasingly complex neuroscientific questions the technical improvements in acquisition must be matched with novel data analysis methods. In this thesis we examine different applications of machine learning to the processing of fMRI data. We propose novel extensions and investigate the theoretical properties of different models. % The goal of an fMRI experiments is to answer a neuroscientific question. However, it is usually not possible to perform hypothesis testing directly on the data output by the fMRI scanner. Instead, fMRI data enters a processing pipeline in which it suffers several transformations before conclusions are drawn. Often the data acquired through the fMRI scanner follows a feature extraction step in which time-independent activation coefficients are extracted from the fMRI signal. The first contribution of this thesis is the introduction a model named Rank-1 GLM (R1-GLM) for the joint estimation of time-independent activation coefficients and the hemodynamic response function (HRF). We quantify the improvement of this approach with respect to existing procedures on different fMRI datasets. The second part of this thesis is devoted to the problem of fMRI-based decoding, i.e., the task of predicting some information about the stimuli from brain activation maps. From a statistical standpoint, this problem is challenging due to the high dimensionality of the data, often thousands of variables, while the number of images available for training is small, typically a few hundreds. We examine the case in which the target variable consist of discretely ordered values. The second contribution of this thesis is to propose the following two metrics to assess the performance of a decoding model: the absolute error and pairwise disagreement. We describe several models that optimize a convex surrogate of these loss functions and examine their performance on different fMRI datasets. Motivated by the success of some ordinal regression models for the task of fMRI-based decoding, we turn to study some theoretical properties of these methods. The property that we investigate is known as consistency or Fisher consistency and relates the minimization of a loss to the minimization of its surrogate. The third, and most theoretical, contribution of this thesis is to examine the consistency properties of a rich family of surrogate loss functions that are used in the context of ordinal regression. We give sufficient conditions for the consistency of the surrogate loss functions considered. This allows us to give theoretical reasons for some empirically observed differences in performance between surrogates.